These are two terms for the same field, and refer to a manual type of medicine (i.e. medicine performed through the hands). It is practiced by osteopathic physicians (D.O.s) as an adjunct therapy to other medicine, and is most commonly used to assist with musculoskeletal pain and chronic pain. There are many types of techniques which range from high velocity techniques (which produce cracks and are somewhat similar to the types of techniques used by chiropractors), to slow techniques employing a patient's own muscles, to soft tissue techniques which resemble massage.
Not all DOs practice OMM, particularly DOs who have specialized in fields such a cardiology, but many primary care physician DOs do practice it to some extent, and those that specialize in neuromuscular medicine practice it almost exclusively.
The American Osteopathic Association's web site can provide you with more information and help you to find a D.O. in your area if you are interested in this type of medicine:
http://www.osteopathic.org